A380725 Positive integers k whose sum of digits equals the square of their number of digits.

1, 13, 22, 31, 40, 108, 117, 126, 135, 144, 153, 162, 171, 180, 207, 216, 225, 234, 243, 252, 261, 270, 306, 315, 324, 333, 342, 351, 360, 405, 414, 423, 432, 441, 450, 504, 513, 522, 531, 540, 603, 612, 621, 630, 702, 711, 720, 801, 810, 900, 1069, 1078, 1087, 1096, 1159, 1168, 1177, 1186, 1195

Offset

1,2

Comments

This is a finite sequence since if k is L digits long then its sum of digits is at most 9*L which is < L^2 for L > 9.

Links

Anwar Hahj Jefferson-George, Table of n, a(n) for n = 1..74583

Mathematica

Select[Range[1200], DigitSum[#]==IntegerLength[#]^2&] (* James C. McMahon, Feb 18 2025 *)

Prog

(Rust)
/// Is the term a valid entry in a380725
pub fn a380725_predicate(mut k: usize) -> bool {
    let base = 10usize;
    let mut len = 0usize;
    let mut digit_sum = 0usize;
    while k > 0 {
        let digit = k.rem_euclid(base);
        k /= base;
        digit_sum += digit;
        len += 1;
    }
    digit_sum == len.pow(2u32)
}
(PARI) isok(k) = my(d=digits(k)); vecsum(d) == sqr(#d); \\ Michel Marcus, Feb 08 2025
(Python)
def ok(n): return sum(map(int, s:=str(n))) == len(s)**2
print([k for k in range(2000) if ok(k)]) # Michael S. Branicky, Feb 08 2025

Crossrefs

Cf. A007953 (sum of digits), A061384.

Sequence in context: A351291 A374254 A336263 * A059408 A164455 A164504

Adjacent sequences: A380722 A380723 A380724 * A380726 A380727 A380728

Keyword

nonn,base,fini,full,easy,new

Author

Anwar Hahj Jefferson-George, Jan 30 2025

Status

approved